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Globally stable blowup profile for supercritical wave maps in all dimensions.
Calc Var Partial Differ Equ
January 2025
Faculty of Mathematics, Bielefeld University, Universitätsstr. 25, 33615 Bielefeld, Germany.
We consider wave maps from the -dimensional Minkowski space into the -sphere. It is known from the work of Bizoń and Biernat (Commun Math Phys 338(3): 1443-1450, 2015) that in the energy-supercritical case, i.e.
View Article and Find Full Text PDFDesign of a Half-Mode Substrate-Integrated Waveguide (HMSIW) Multimode Resonator Bandpass Filter Using the Minkowski Fractal for C-Band Applications.
Micromachines (Basel)
November 2024
Department of ECE, Jaypee Institute of Informaton Technology, Noida 201309, UP, India.
A substrate-integrated waveguide (SIW) bandpass filter (BPF) with extraordinary selectivity and an adequate upper stopband for C-band Satellite Communication (SATCOM) applications is proposed in this paper. The design comprises comb-shaped slots engraved on a half-mode SIW (HMSIW) that constitute a multimode resonator (MMR). Its performance is further ameliorated by applying the first and second iterations of the Minkowski fractal curve in the ground plane as a defected ground structure (DGS).
View Article and Find Full Text PDFCelestial Holography Revisited.
Phys Rev Lett
December 2024
Dipartimento di Fisica "Ettore Pancini," Università degli Studi di Napoli Federico II, Monte Sant'Angelo, Via Cintia, 80126 Napoli, Italy; INFN, Sezione di Napoli, Monte Sant'Angelo, Via Cintia, 80126 Napoli, Italy; and Scuola Superiore Meridionale, Università degli Studi di Napoli Federico II, Largo San Marcellino 10, 80138 Napoli, Italy.
We revisit the prescription commonly used to define holographic correlators on the celestial sphere of Minkowski space as an integral transform of flat space scattering amplitudes. We propose a new prescription according to which celestial holographic correlators are given by the Mellin transform of bulk time-ordered correlators with respect to the radial direction in the hyperbolic slicing of Minkowski space, which are then extrapolated to the celestial sphere along the hyperbolic directions. This prescription is analogous to the extrapolate definition of holographic correlators in AdS/CFT and, like in AdS, is centered on (off-shell) correlation functions as opposed to (on-shell) S-matrix elements.
View Article and Find Full Text PDFA new view of spaces and their properties in the sense of non-Newtonian measure.
PLoS One
December 2024
Department of Mathematics & Statistics, Jordan University of Science and Technology, Irbid, Jordan.
This study presents a novel approach to metric spaces through the lens of geometric calculus, redefining traditional structures with new operations and properties derived from non-Newtonian measures. Specifically, we develop and prove geometric versions of the Hölder and Minkowski inequalities, which provide foundational support for applying these spaces in analysis. Additionally, we establish key relationships between geometric and classical metric spaces, examining concepts such as openness, closedness, and separability within this geometric framework.
View Article and Find Full Text PDFThe quantum optics of media.
Philos Trans A Math Phys Eng Sci
December 2024
School of Physics and Astronomy, University of Glasgow, Glasgow G128QQ, UK.
The quantum theory of light in real media requires attention to a number of physical features. Even in near-transparent dielectrics, we have to incorporate dispersion, losses and the effects of interfaces. Here, we review the quantization of light in a dielectric and see how this affects radiative processes and light propagation.
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